Space and Time By David R. Maidment with contributions from Steve Kopp, Steve Grise, and Tim Whiteaker

Space and Time Introductory concepts Discrete space-time model – Arc Hydro Temporal Geoprocessing Continuous space-time model – netCDF Tracking Analyst

Space and Time Introductory concepts Discrete space-time model – Arc Hydro Temporal Geoprocessing Continuous space-time model – netCDF Tracking Analyst

4 Linking GIS and Water Resources GIS Water Resources Water Environment (Watersheds, gages, streams) Water Conditions (Flow, head, concentration)

Data Cube Space, L Time, T Variables, V D “What” “Where” “When” A simple data model

6 Space, FeatureID Time, TSDateTime Variables, TSTypeID TSValue Discrete Space-Time Data Model ArcHydro

Continuous Space-Time Model – NetCDF (Unidata) Space, L Time, T Variables, V D Coordinate dimensions {X} Variable dimensions {Y}

CUAHSI Observations Data Model A relational database at the single observation level (atomic model) Stores observation data made at points Metadata for unambiguous interpretation Traceable heritage from raw measurements to usable information Streamflow Flux tower data Precipitation & Climate Groundwater levels Water Quality Soil moisture data

Pre Conference Seminar 9 ODM and HIS in an Observatory Setting e.g.

Space, Time, Variables and Observations Variables (VariableID) Space (HydroID) Time Observations Data Model Data from sensors (regular time series) Data from sensors (regular time series) Data from field sampling (irregular time points) Data from field sampling (irregular time points) An observations data model archives values of variables at particular spatial locations and points in time

Space, Time, Variables and Visualization Variables (VariableID) Space (HydroID) Time Vizualization Map – Spatial distribution for a time point or interval Map – Spatial distribution for a time point or interval Graph – Temporal distribution for a space point or region Graph – Temporal distribution for a space point or region Animation – Time-sequenced maps Animation – Time-sequenced maps A visualization is a set of maps, graphs and animations that display the variation of a phenomenon in space and time

Space, Time, Variables and Simulation Variables (VariableID) Space (HydroID) Time Process Simulation Model A space-time point is unique A space-time point is unique At each point there is a set of variables At each point there is a set of variables A process simulaton model computes values of sets of variables at particular spatial locations at regular intervals of time

Space, Time, Variables and Geoprocessing Variables (VariableID) Space (HydroID) Time Geoprocessing Interpolation – Create a surface from point values Interpolation – Create a surface from point values Overlay – Values of a surface laid over discrete features Overlay – Values of a surface laid over discrete features Temporal – Geoprocessing with time steps Temporal – Geoprocessing with time steps Geoprocessing is the application of GIS tools to transform spatial data and create new data products

Space, Time, Variables and Statistics Variables (VariableID) Space (HydroID) Time Statistical distribution Represented as {probability, value} Represented as {probability, value} Summarized by statistics (mean, variance, standard deviation) Summarized by statistics (mean, variance, standard deviation) A statistical distribution is defined for a particular variable defined over a particular space and time domain

Space, Time, Variables and Statistical Analysis Variables (VariableID) Space (HydroID) Time Statistical analysis Multivariate analysis – correlation of a set of variables Multivariate analysis – correlation of a set of variables Geostatistics – correlation space Geostatistics – correlation space Time Series Analysis – correlation in time Time Series Analysis – correlation in time A statistical analysis summarizes the variation of a set of variables over a particular domain of space and time

Pre Conference Seminar 16 CUAHSI Observations Data Model Space-Time Datasets Sensor and laboratory databases From Robert Vertessy, CSIRO, Australia

Space and Time Introductory concepts Discrete space-time model – Arc Hydro Temporal Geoprocessing Continuous space-time model – netCDF Tracking Analyst

Space-Time Cube TSDateTime TSTypeID TSValue FeatureID Time Space Variable Data Value

Time Series Data

Time Series of a Particular Type

A time series for a particular feature

A particular time series for a particular feature

All values for a particular time

MonitoringPointHasTimeSeries Relationship

TSTypeHasTimeSeries

Arc Hydro TSType Table Type Index Variable Name Type Of Time Series Info Regular or Irregular Units of measure Time interval Recorded or Generated Arc Hydro has 6 Time Series DataTypes 1.Instantaneous 2.Cumulative 3.Incremental 4.Average 5.Maximum 6.Minimum

Instantaneous Cumulative Average Incremental Maximum Minimum Time Series Types

A Theme Layer Synthesis over all data sources of observations of a particular variable e.g. Salinity 28

Texas Salinity Theme 7900 series 347,000 data 7900 series TPWD 3400 TCEQ 3350 TWDB

Copano and Aransas Bay Salinity Number of Data 0 – – – – – 3000 Copano Bay Aransas Bay 30

Texas Daily Streamflow Theme USGS Data 1138 sites (400 active) 31

Austin – Travis Lakes Streamflow Years of Data 0 – – – – –

Texas Water Temperature Theme 22,700 series 966,000 data 33

Austin – Travis Lakes Water Temperature Number of Data 0 – – – – –

Data from Individual Sites

HydroPortal to access Themes

Space and Time Introductory concepts Discrete space-time model – Arc Hydro Temporal Geoprocessing Continuous space-time model – netCDF Tracking Analyst

Time Series {value, time} Attribute Series {featureID, value, time} Raster Series {raster, time} Feature Series {shape,value, time} Four Panel Diagram

Time series from gages in Kissimmee Flood Plain 21 gages measuring water surface elevation Data telemetered to central site using SCADA system Edited and compiled daily stage data stored in corporate time series database called dbHydro Each time series for each gage in dbHydro has a unique dbkey (e.g. ahrty, tyghj, ecdfw, ….)

Compile Gage Time Series into an Attribute Series table

Hydraulic head Hydraulic head is the water surface elevation in a standpipe anywhere in a water system, measured in feet above mean sea level h Land surface Mean sea level (datum)

Map of hydraulic head X Y Z Hydraulic head, h x y h(x, y) A map of hydraulic head specifies the continuous spatial distribution of hydraulic head at an instant of time

Time sequence of hydraulic head maps x y z Hydraulic head, h t1t1 t2t2 t3t3

Attribute Series to Raster Series

Inundation h L d Depth of inundation = d IF (h - L) > 0 then d = h – L IF (h – L) < 0 then d = 0

Inundation Time Series t h(x,y,t) L T (x,y) Time d(x,y,t) d(x,y,t) = h(x,y,t) – L T (x,y)

Ponded Water Depth Kissimmee River June 1, 2003

Depth Classification DepthClass

Feature Series of Ponded Depth

Attribute Series for Habitat Zones

Space and Time Introductory concepts Discrete space-time model – Arc Hydro Temporal Geoprocessing Continuous space-time model – netCDF Tracking Analyst

Multidimensional Data Data cube (3D) or hypercube (4D,5D…) Temperature varying with time Temperature varying with time and altitude X Y T

Multidimensional Data Time = 1 Time = 2 Time = 3

Multidimensional Data Time = 1 Time = 2 Time = 3

Data Cube Time Slices Multidimensional Data Time = 1 Time = 2 Time = 3

Multidimensional Data Includes variation in (x,y,z,t)

What is NetCDF? NetCDF (network Common Data Form) A platform independent format for representing multi- dimensional array-orientated scientific data. Self Describing - a netCDF file includes information about the data it contains. Direct Access - a small subset of a large dataset may be accessed efficiently, without first reading through all the preceding data. Sharable - one writer and multiple readers may simultaneously access the same netCDF file. NetCDF is new to the GIS community but widely used by scientific communities for around many years

What is a NetCDF file? NetCDF is a binary file A NetCDF file consists of: Global Attributes: Describe the contents of the file Dimensions:Define the structure of the data (e.g Time, Depth, Latitude, Longitude) Variables:Holds the data in arrays shaped by Dimensions Variable Attributes: Describes the contents of each variable CDL (network Common Data form Language) description takes the following form netCDF name { dimensions:... variables:... data:... }

Storing Data in a netCDF File

NetCDF Data Sources Community Climate Systems Model (CCSM) The CCSM is fully-coupled, global climate model that provides state-of-the-art computer simulations of the Earth's past, present, and future climate states. 100 yrs of climate change forecast data ( ) Control runs ( ) and scenario runs Temperature, precipitation flux, surface snow thickness, snowfall flux, cloud water content, etc. Program for Climate Model Diagnosis and Intercomparison (PCMDI)

NetCDF Data Sources Vegetation and Ecosystem Modeling and Analysis Project (VEMAP) VEMAP was a large, collaborative, multi-agency program to simulate and understand ecosystem dynamics for the continental United States. The VEMAP Data Portal is a central collection of files maintained and serviced by the NCAR Data Group Climate data interval: Annual, monthly, and daily. Data type: Historical and model results Data: Temperature, irradiance, precipitation, humidity, incident solar radiation, vapor pressure, elevation, land area, vegetation, water holding capacity of soil, etc.

NetCDF Data Sources British Atmospheric Data Center (BADC) The role of the BADC is to assist UK atmospheric researchers to locate, access and interpret atmospheric data. Many datasets are publicly available but datasets marked with key symbol have restricted access. Datasets are organized by projects or organizations. Climatology Interdisciplinary Data Collection (CIDC) has monthly means of over 70 Climate Parameters. Met Office - Historical Central England Temperature Data has the monthly series, which begins in 1659, is the longest available instrumental record of temperature in the world. The daily series begins in 1772.

NetCDF Data Sources National Oceanic & Atmospheric Administration (NOAA) National Digital Forecast Database (NDFD) Radar Integrated Display with Geospatial Element (RIDGE) Precipitation Analysis Climate Diagnostics Center NCDC THREDDS Catalog NCDC NCEP Stage IV Radar Rainfall

NetCDF in ArcGIS NetCDF data is accessed as Raster Feature Table Direct read (no scratch file) Exports GIS data to netCDF

Gridded Data Raster Point Features

NetCDF Tools Toolbox: Multidimension Tools Make NetCDF Raster Layer Make NetCDF Feature Layer Make NetCDF Table View Raster to NetCDF Feature to NetCDF Table to NetCDF Select by Dimension

Space and Time Introductory concepts Discrete space-time model – Arc Hydro Temporal Geoprocessing Continuous space-time model – netCDF Tracking Analyst

Simple Events –1 feature class that describes What, When, Where Complex Event –1 feature class and 1 table that describe What, When, Where Arc Hydro

Simple Event IDTimeGeometryValue 1T1X1,Y10.1 2T2X2,Y20.3 1T3X3,Y30.7 2T4X4,Y40.4 3T5X5,Y50.5 2T6X6,Y60.2 4T7X7,Y70.1 1T8X8,Y80.8 1T9X9,Y90.3 Unique Identifier for objects being tracked through time Time of observation (in order)Geometry of observation Observation

Complex Event (stationary version) IDGeometry 1X1,Y1 2X2,Y2 3X3,Y3 4X4,Y4 IDTimeValue 1T10.1 2T20.3 1T30.7 2T40.4 3T50.5 2T60.2 4T70.1 1T80.8 1T90.3 The object maintains its geometry (i.e. it is stationary) Cases 1, 2, 3, 4, 5

Complex Event (dynamic version) IDGage Number IDGeometryTimeValue 1X1,Y1T10.1 2X2,Y2T20.3 1X3,Y3T30.7 2X4,Y4T40.4 3X5,Y5T50.5 2X6,Y6T60.2 4X7,Y7T70.1 1X8,Y8T80.8 1X9,Y9T90.3 The object’s geometry can vary with time (i.e. it is dynamic) Cases 6 and 7

Tracking Analyst Display

Feature Class and Time Series Table

Temporal Layer Shape from feature class is joined to time series value from Time Series table

Summary Concepts Hydrologic variables are defined as a function of space and time Although space and time seem alike as independent dimensions they are not: –Space can be discrete or continuous and is multidimensional –Time is one-dimensional This leads to idea of spatially-referenced time series of data

Summary Concepts (II) In Arc Hydro, discrete spatial features are associated with time series values through a HydroID-FeatureID relationship Time series associated with individual features become Attribute Series associated with a Feature class Attribute series can be transformed to Raster Series and Feature Series by temporal geoprocessing (Four panel diagram)

Summary Concepts (III) ArcGIS explicitly supports time representations through –By allowing operations on netCDF files for spatially continuous fields –By allowing visualization of moving features using Tracking Analyst